Various applications using an optical Fourier transform technique to convert the temporal waveform of an optical pulse into the shape of a frequency spectrum thereof or to convert the shape of the frequency spectrum of the optical pulse into the temporal waveform thereof have been proposed in the fields of ultrahigh-speed optical communication, ultra-short pulse mode-locked laser, optical signal processing and the like. For example, in the ultrahigh-speed optical communication, there have been proposed applications to the reduction of random fluctuation (timing jitter) of a time position of each pulse in a signal optical pulse train (see, for example, non-patent document 1), the compensation of polarization mode dispersion (see, for example, non-patent document 2), and the like. Besides, the optical Fourier transform technique is effective also in the suppression of timing jitter of an ultra-short pulse emitted from a mode-locked laser (for example, non-patent document 3). Besides, there is a document disclosing the generation of a quadratic function type optical pulse using an optical fiber amplifier having a normal dispersion (see, for example, non-patent document 4).
The present inventor has filed applications on waveform distortion-free transmission in which a time and a frequency are replaced with each other at the receiver side and transmission data is completely reproduced, since in general, even if any linear distortion effects exist in an optical fiber, the spectrum shape of a pulse is invariable (Japanese Patent Application No. 2003-23973 “Optical Transmission Method and Optical Transmission Device”, Japanese Patent Application No. 2003-181964 “OTDM Transmission Method and Device”), optical pulse compression and optical function generation (Japanese Patent Application No. 2003-109708 “Optical pulse Compressor and Light Function Generator, Optical pulse Compression Method and Light Function Generation Method”). Besides, the inventor has filed an application on a method and device which generates an optical pulse expressed by a quadratic function type without using an optical fiber amplifier (Japanese Patent Application No. 2003-387563 “Optical pulse Generation Method and Optical pulse Compression Method, etc.”). The contents of these applications can be incorporated in the present specification by reference.
FIG. 1 shows a structural example of a circuit conventionally used to perform optical Fourier transform. In the figure, this circuit includes a phase modulator (LN phase modulator) 2 using the Pockels effect in an electro-optic crystal such as LiNbO3 crystal, and a dispersive medium 3 having a dispersion amount D. Incidentally, when the dispersion parameter of the dispersive medium 3 is β2[ps2/km] and the length is L[km], the dispersion amount is given by D=β2L[ps2]. Besides, in the figure, a solid line indicates an optical pulse, and a dotted line indicates an electric signal. An optical fiber, a diffraction grating pair, a fiber Bragg grating or the like is used as the dispersive medium 3. The peak of a modulation characteristic of the phase modulator 2 is made to coincide with the center position of an optical pulse. The magnitude of a chirp (chirp rate K) applied to a pulse by the LN phase modulator 2 can be obtained in a manner as described below. When voltage V(t)=V0 cos(ωmt) is applied to the phase modulator 2, a light phase change amount Δφ(t) caused by a change in refractive index due to the electro-optic effect is given by
                                 [                      Mathematical            ⁢                                                  ⁢            formula            ⁢                                                  ⁢            1                    ]                                                                                                              Δ              ⁢                                                          ⁢              ϕ              ⁢                                                          ⁢                              (                t                )                                      =                          M              ⁢                                                          ⁢              cos              ⁢                                                          ⁢                              (                                                      ω                    m                                    ⁢                  t                                )                                              ,                      M            =                                          π                ⁢                                                                  ⁢                                  V                  0                                                            V                π                                                                          (          1          )                    Where Vπ denotes a half-wavelength voltage (applied voltage necessary to rotate the phase of light by π), ωm denotes the drive frequency of the phase modulator, and V0 denotes the amplitude of the voltage. When expression (1) is expanded into Taylor series in the vicinity (t=0) of the center of the pulse, it can be approximated by
                                 [                      Mathematical            ⁢                                                  ⁢            formula            ⁢                                                  ⁢            2                    ]                                                                                                              Δ              ⁢                                                          ⁢                              ϕ                ⁡                                  (                  t                  )                                                      =                                          M                ⁡                                  (                                      1                    -                                                                                            ω                          m                          2                                                2                                            ⁢                                              t                        2                                                                              )                                            =                                                Δ                  ⁢                                                                          ⁢                  ϕ                  ⁢                                                                          ⁢                                      (                    0                    )                                                  +                                                      K                    2                                    ⁢                                      t                    2                                                                                ,                      K            =                                          -                M                            ⁢                                                          ⁢                              ω                m                2                                                                          (          2          )                    That is, by the LN phase modulator, a frequency chirp
                                 [                      Mathematical            ⁢                                                  ⁢            formula            ⁢                                                  ⁢            3                    ]                                                                                                Δ            ⁢                                                  ⁢            ω            ⁢                                                  ⁢                          (              t              )                                =                                    -                                                                    ∂                    Δ                                    ⁢                                                                          ⁢                  ϕ                                                  ∂                  t                                                      =                                          -                K                            ⁢                                                          ⁢              t                                                                                which has the chirp rate K and is approximately linear is applied to the optical pulse.
In FIG. 1, the optical pulse having a temporal waveform u(t) and a frequency spectrum U(ω) is first divided into two parts by an optical coupler 1, and the one part is launched to the LN phase modulator 2. The other part is launched to a clock extraction circuit 4, and a clock signal (sinusoidal signal) is extracted from the pulse train. The emitted signal is applied to the LN phase modulator 2 through a phase shifter 5 and an electrical amplifier 6, so that the LN phase modulator 2 is driven. The phase shifter 5 is inserted in order to apply phase modulation to the optical pulse optimally synchronously. The electric amplifier 6 is for driving the LN phase modulator 2.
The optical pulse launched to the LN phase modulator 2 is given the linear chirp Δω(t)=−Kt, and as a result, at each time position of the pulse waveform, it acquires a frequency shift with a magnitude proportional to the time. Further, the linearly chirped pulse is launched to the dispersive medium 3. In the dispersive medium 3, a time delay (group delay in the pulse) depending on frequency by a group-velocity dispersion is given to the temporal waveform of the optical pulse. Since the optical pulse is previously given the linear chirp in the LN phase modulator 2, the respective frequency components of the optical pulse are separated in the dispersive medium 3 to different positions in the time domain. As a result, when the dispersion amount D with respect to the chirp rate K is selected to be D=1/K, the waveform in proportion to a spectrum shape U(ω) (where ω=t/D) of the optical pulse before optical Fourier transform is obtained in the time domain at the output of the dispersive medium 3.
Non-patent document 1: L. F. Mollenauer and C. Xu, “Time-lens timing-jitter compensator in ultra-long haul DWDM dispersion managed soliton transmissions,” in Conference on Lasers and Electro-Optics (CLEO) 2002, paper CPDB1 (2002).
Non-patent document 2: M. Romagnoli, P. Franco, R. Corsini, A. Schiffini, and M. Midrio, “Time-domain Fourier Optics for polarization-mode dispersion compensation,” Optics Letters, vol. 24, no. 17, pp. 1197-1199 (1999).
Non-patent document 3: L. A. Jiang, M. E. Grein, H. A. Haus, E. P. Ippen, and H. Yokoyama, “Timing jitter eater for optical pulse trains,” Optics Letters, vol. 28, no. 2, pp. 78-80 (2003).
Non-patent document 4: M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. Vol. 84, pp. 6010-6013 (2000).